US5115479A  Image data processing method for compressing an image by approximating curves using a polynomial  Google Patents
Image data processing method for compressing an image by approximating curves using a polynomial Download PDFInfo
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 US5115479A US5115479A US07768465 US76846591A US5115479A US 5115479 A US5115479 A US 5115479A US 07768465 US07768465 US 07768465 US 76846591 A US76846591 A US 76846591A US 5115479 A US5115479 A US 5115479A
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 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
 G06T11/00—2D [Two Dimensional] image generation
 G06T11/20—Drawing from basic elements, e.g. lines or circles
 G06T11/203—Drawing of straight lines or curves

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
 G06F—ELECTRICAL DIGITAL DATA PROCESSING
 G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
 G06F17/10—Complex mathematical operations
 G06F17/17—Function evaluation by approximation methods, e.g. inter or extrapolation, smoothing, least mean square method
Abstract
M(X,Y)=A(1t).sup.3 +(cP(c3)A)(1t).sup.2 t+(dQ(d3)E)(1t)t.sup.2
Description
This application is a continuation of U.S. patent application Ser. No. 07/391,788, filed Aug. 9, 1989, now abandoned.
The present invention generally relates to processing of image data and more particularly to an image data processing method for compressing twodimensional curve image data and for expanding the information thus compressed.
In a field of image processing, a twodimensional curve image is usually decomposed into a number of segments, and vectors are assigned in correspondence to each of the segments. Thus, the curve is represented by a number of vectors each corresponding to the segment. In such a method, when the curve has a large curvature, a large number of vectors are needed. Associated therewith, information to be processed is increased, which causes a difficulty in transmission or storage in memory. Further, such a method has a problem of synthesizing a smooth curve as the synthesis of the curve is made on the basis of connection of a number of these segments.
In order to avoid these problems, there has been proposed to use the Bezier's equation for approximation of the curve. According to this method, the curve is approximated by the following equation:
B(X,Y)=A(1t)+3P'(1t).sup.2 t +3Q(1t)t.sup.2 +Et.sup.3 ( 1)
where B(X,Y) represents a coordinate of the twodimensional curve, A and E respectively stand for an initial point and a terminal point of the curve, P' and Q' respectively stand for an initial point and a terminal point of a line which characterizes the shape of the curve and also tangential directions at points A and E, and t stands for a parameter specifying position of a point on the curve between the point A and the point E. The parameter t assumes a value zero (0) at the point A and a value one (1) at the point E. According to Eq.(1), the curve is characterized by only four points A, E, P' and Q'.
FIGS. 1(A) and (B) show typical examples of such curves B_{1} B_{6}, or B_{1} 'B_{6} ' wherein the shape of the curve is determined by the coordinate of the initial point A and the terminal point E as well as initial points P_{1} 'P_{6} ' and terminal points Q_{1} 'Q_{6}, corresponding to the points P' and Q'.
As can be seen from these drawings, segments P1'Q1', P2'Q2', P3'Q3' . . . respectively connecting the points P_{1} ' and Q_{1} ', P_{2} ' and Q_{2} ', P_{3} ' and Q_{3} ' . . . do not make contact with respective curves and because of this, there arises a problem in that the curve generated from given control points does not closely reproduce the original image formed in a bit map. In relation with this, automatic contour coding or data compression of the image becomes difficult as the curves which can closely represent the image on the bit map has to be specified by the control points which are not on the edge of the image. Further, when the curve is located close to a marginal region of the image to be processed, there appears a case in which the points P' and Q' are located outside of image field secured for storing a bit map. In such a case, one has to provide additional memory field in correspondence to coordinates outside of the image field for accommodating these coordinate data. Such a procedure invites unwanted increase of memory space or amount of information to be processed.
Accordingly, it is a general object of the present invention to provide a novel and useful image processing method wherein the aforementioned problems are eliminated.
Another and more specific object of the present invention is to provide an image processing method wherein a twodimensional curve is compressed effectively without losing smoothness of the curve when the curve is reproduced.
Another object of the present invention is to reproduce an image which closely represents an original image from a compressed image data.
Another object of the present invention is to provide a method of image data compression wherein determination of control points for describing a given image is performed easily and automatically on a basis of original image represented in a form of bit map.
Another object of the present invention is to provide an image processing method for compressing an information of a twodimensional curve by four independent coordinate parameters, first one specifying an initial point of the curve, second one specifying a terminal point of the curve, third one located on a tangential passing through the initial point of the curve, and fourth one located on another tangential passing through the terminal point of the curve, wherein a line specified by the last two coordinate parameters maintains a tangential contact with the curve, and further for reproducing the image thus compressed according to an equation:
M(X,Y)=A(1t).sup.3 +(cP(c3)A)(1t).sup.2 t +(dQ(d3)E)(1t)t.sup.2 +E
where A stands for the first coordinate parameter, E stands for the second coordinate parameter, P stands for the third coordinate parameter, Q stand for the fourth coordinate parameter, c and d are predetermined coefficients, and t is a parameter between zero and one representing position of a point on the curve. According to the present invention, processing of the twodimensional curve becomes easy as the last mentioned line connecting the third and fourth coordinate parameters maintains the tangential contact with the curve and the coordinate parameters defining the line are determined as an intersection of said line with a tangential of the curve passing through the initial point of the curve or with another tangential passing through the terminal point of the curve. The detection of these tangentials including said line is easily performed automatically by edge detection. As the image reproduced by these four coordinate parameters according to the aforementioned equation makes a tangential contact with the line connecting the third and fourth coordinate parameters, the reproduced image closely represents the original image formed on a bit map. Further, the lines characterizing the shape of the curve does not move outside of image field secured for the image and the memory space hitherto necessary when the Bezier's equation is used for storing coordinates of the lines which located outside of the image field is saved.
Other objects and further features of the present invention will become apparent from the following detailed description for preferred embodiments when read in conjunction with attached drawings.
FIGS. 1(A) and (B) are diagrams showing a prior art data compression procedure using the Bezier's equation for a number of curves;
FIGS. 2(A)(C) are diagrams showing a principle of data compression according to the present invention for various twodimensional curves;
FIG. 3 is a diagram showing the data compression for a case of Japanese letter "tsu" according to an embodiment of the present invention;
FIG. 4 is an enlarged view showing the compression of data of FIG. 3 in detail;
FIG. 5 is a block diagram showing a procedure for a rastervector conversion;
FIG. 6 is a block diagram showing a procedure for a vectorraster conversion; and
FIG. 7 is a block diagram showing a printer controller to which the present invention is applied.
First, the principle of the present invention will be described with reference to FIG. 2(A)(C). According to the present invention, a twodimensional curve M(X, Y) is approximated by an equation:
M(X, Y)=A(1t).sup.3 +(cP(c3)A)(1t).sup.2 t +(dQ(d3)E)(1t)t.sup.2 +Et.sup.3 (2)
where A and E stand for the initial and terminal points of the twodimensional curve, P and Q give the tangential direction at A and E or line PQ making a tangential contact with the twodimensional curve, and t stands for a parameter which changes its value between zero and one. Similarly to Eq.(1), the parameter t changes between zero and one. Further, c and d in Eq.(2) are predetermined coefficients. Thus, Eq.(2) has a feature in that the line PQ maintains a tangential contact with the curve M(X, Y). The initial point A and the terminal point E are immediately found out by edge detection. The points P and Q, too, is easily determined by detecting a peak point of the curve and by finding out a tangential passing through the peak point. Eq.(2) reproduces the twodimensional curve with excellent precision particularly when the coefficients c and d are set as c=d=4. The curve represented by such an equation has a preferable feature in that the line PQ extends parallel to a line AE connecting the points A and W.
FIGS. 2(A)(C) show various curves which are defined by the points A, E, P and Q according to Eq.(2), in which FIGS. 2(A) and (B) respectively show six sets of such curves M_{1} M_{6}. In the curves M_{1} M_{6}, the coordinate of the points P and Q are changed from P_{1} to P_{6} and from Q_{1} to Q_{6}, respectively. Note that the point P is determined as an intersection of a tangential line AP passing through the initial point A and the line PQ. Similarly, the point Q is determined as an intersection of a tangential line EQ passing through the terminal point E and the line PQ. FIG. 2(C) on the other hand shows eight such curves corresponding to the coordinate of the points P and Q changing from to P and from Q_{1} to Q_{8} for a case that the point A agrees with the point E. Note that FIG. 2(A) shows a case in which the line AE is parallel to the line PQ' and FIG. 2(B) shows a case in which the line PQ is not parallel to the line AE. Here, the line PQ symbolically represents a group of lines P_{1} Q_{1}, P_{2} Q_{2}, P_{3} Q_{3}, . . .
As the curves shown in FIGS. 2(A)(C) have a common feature in that the line PQ makes a tangential contact with the curve itself, the reproducing of the curve according to Eq.(2) becomes significantly easier and the risk that the points P and Q move outside of the field of the image is avoided.
For the case of FIG. 2(A) where the line AE is parallel to the line PQ' the condition c=d=4 is satisfied as already described and Eq.(2) can be rewritten as ##EQU1##
For the case of FIGS. 2(B) and (C) where the line AE and PQ are not parallel, the coefficient c and d generally fall in a range between three and four. In the most case, the value of the coefficient becomes about 3.9 which is quite close to four. This means that the curve obtained by applying Eq.(3) to the case where the line AE and the line PQ are not parallel satisfactorily approximates the original curve without visually noticeable deformation.
Next, a first embodiment of the present invention will be described with reference to FIG. 3 showing an example of data compression for a font of Japanese letter (pronounced "tsu"). The font comprises a first curve portion S1 inscribing in a quadrangle A1A2P1Q1 defined by an initial point A1 and a terminal point A2 as well as other points P1 and Q1 defining a line P1Q1 which, makes a tangential contact with the curve portion S2, and a second curve portion S2 inscribing in a quadrangle A2A3P2Q2 defined by the point A2 acting as the initial point makes a tangential contact with the curve portion S2. Thus, the information which describes the letter can be compressed into two sets of data, one comprising coordinates of the points A1, A2, P1 and Q1 and the other comprising the coordinates of the points A2, A3, P2 and Q2. These points are obtained from the tangentials A1P1, P1Q1, Q1A2 and A2P2, P2Q2, Q2A3 and A3A2. As already noted, the detection of these tangentials can be made easily and automatically from the font formed in the bit map by edge detection.
When the two curves are continuous, the terminal point A2 of the curve portion S1 and the initial point A2 of the curve portion S2 become identical. Thus, a curve comprising n curve portions can generally be represented by n+1 coordinates specifying the initial and terminal points A_{i} (i=1, 2, 3, . . . , n, n+1) of the curve portions and two coordinates for each of the n curve portions. Thus, the curve can after all be specified by 3n+1 (=n+1+2n) points.
In the case that the coefficients c and d are set to satisfy the relation c=d=4, a line int A2 of the curve portion S1 becomes parallel to the line P1Q1 making a tangential contact with the curve portion S1. Thus, the coordinate of the terminal point Q1 is given by a coordinate pl of the initial point P1 in combination with a distance s_{1} of the point Q1 measured from the point P1.
For the case of the second curve portion S2, the initial point P2 is located on an extension of a line Q1A2 connecting the point Q1 and the point A2 as is clearly illustrated in FIG. 3, and therefore, the coordinate of the point P2 can be obtained by the coordinate of the point A2 in combination with a distance s2 of the point P2 measured from the point A2.
The position of the point P2 thus represented in terms of the distance s_{2} is then converted to x and ycoordinates by using a general relation x=s.cosθ and y=s.sinθ, where θ stands for an angle defined between the line connecting the points and the abscissa as defined in FIG. 3 and s stands for the distance between the two points. By using the distance data s which is a scaler quantity, one can reduce the information to be processed as compared to a case in which the coordinate of the points is represented by vectors each comprising two components.
Alternatively, one may obtain the coordinate of the points by using a data set comprising a distance data and an argument data of a point with respect to an immediately preceding point. Thus, the coordinate of the point P2 for example is obtained by adding the x and ycoordinates to the corresponding coordinates of the point Q1 which in turn are obtained by adding the xand ycoordinates obtained similarly to the x and ycoordinates of the point P1. When adopting this method, one may quantize the argument data into sixteen directions for example, each separated by 22.5 degrees. In this case, the argument can be digitized by four bit data and the information to be processed is further reduced.
When synthesizing the curve, Eq.(2) is used for each of the curve portions and the coordinate of the dots used for displaying the curve portions S1 and S2 are calculated with a sufficient density. The dots thus obtained are connected by line segments. It is needless to say that the more the number of dots, the more the smoothness of the line is improved. As the curve reproduced by Eq.(2) always makes tangential contact with the line PQ defined by the control points P and Q, the reproduced curve from the points A, E, P and Q closely represents the original font.
When decomposing a font into a number of curve portions having different curvatures and line portions having different lengths, the curve is once divided into a number of unit vectors and the segmentation of the curve into the curve portions and the line portions is performed by detecting the change in the direction of the unit vectors.
In order to avoid unwanted excessive use of memory or transmission band arising when applying Eq.(2) or Eq.(3) involving four parameters to a case where the curve includes a substantial proportion of line portions, it is preferred to separate the line portion from the curved portion by detecting the directional change of the unit vector or the curvature. The line portion thus separated is then represented by the two points corresponding to the initial and terminal points.
FIG. 4 shows the data compression of the letter "tsu" for an actual case in which the letter has a finite thickness. After the edge detection of the font "tsu", an edge pattern shown in FIG. 4 is obtained. When the font is represented in a form of bit map, the edge pattern is not smooth but comprises a number of steps. For the sake of simplicity and clarity of the illustration, representation of the edge pattern by stepped line is omitted. The letter comprises a first curve SO defining an outer contour and a second curve SI defining an inner contour of the letter wherein the curve SO comprises a curve portion SO_{1} corresponding to the curve portion S1 of FIG. 3 and a curve portion SO_{2} corresponding to the curve portion S2 of FIG. 3 and the curve SI comprises a curve portion SI_{1} and a curve portion SI_{2}. Similarly to the case of FIG. 3, the curve portion SO_{1} is represented by the points A1 and A2 as well as points PO1 and QO1 corresponding to the points P_{1} and Q_{1}, and the curve portion SO_{2} is represented by the points A2 and A3 as well as points PO2 and QO2 corresponding to the points P2 and Q2. Further, the curve portion SI_{1} is determined by the initial point A1 as well as points PI1, QI1 and a terminal point A4 which correspond to the parameters A, P, Q and E of Eq.(2) respectively. The curve portion SI_{2} is determined by the initial point A4 and terminal point A3 as well as points PI2 and QI2 which correspond to the parameters A, P, Q and E of Eq.(2). Note that the points A1, PI1, QI1 and A4 defines a quadrangle PIIQ1IA4 in which the curve portion SI_{1} inscribes, and the points A4, PI2, QI2 and A3 defines a quadrangle A4PI2Q12A3 in which the curve portion SI_{2} inscribes. As the data compression for the curve portions SO_{1}, SO_{2}, SI_{1} and SI_{2} are identical to that of the curve portions S1 and S2 already described with reference to FIG. 3, further description will be omitted. When these curves are reproduced according to Eq.(2) or (3), area surrounded by the curves SO and SI is filled by dots as usual.
FIG. 5 shows a rastervector conversion procedure for compressing an image data according to Eq.(2) or (3). Referring to the drawing, the image to be compressed is read by raster scanning and the like in a step 101, whereby the read image is stored in a pattern memory in a form of a bit map. Next, a contour of the pattern is extracted from the bit map in a step 102 by edge filtering and the like, and the contour thus obtained is divided into a number of line portions and curve portions on the basis of curvature detection in a step 103. In a step 104, the line portions extracted in the step 103 is compressed into a vector data comprising coordinates of the initial point and terminal point and the curve portions is compressed into a vector data comprising coordinates of the four parameters A, E, P and Q of Eq.(2) or Eq.(3). The vector data thus obtained is then stored in a memory as shown in a step 105.
When the image data compression method of the present invention is applied to a facsimile transmission system, the vector data is transmitted to a reception side where the original image is recovered according to a vectorraster conversion procedure shown in FIG. 6. Referring to FIG. 6, the vector data is read out in a step 201 from a memory storing the received vector data and the contour of the curve portion is reproduced in a step 202 according to Eq.(2) or Eq.(3). The contour of the line portion is reproduced from the coordinate of its initial point and terminal point as already described. In a step 203, the overall contour of the original image is recovered by connecting the contours thus reproduced Further, an area surrounded by the contour of the image thus recovered is filled by dots in a step 204 and a bit map of the dots thus obtained is stored in a pattern memory in a step 205. The bit map thus obtained is converted to a visual image by a printer and the facsimile transmission of the image is completed.
It should be noted that the vector data may be represented by a radial distance and an argument measured from a reference point instead of representing by the ordinary x and y coordinate as already described. Further, when the image is satisfactorily approximated on the assumption that the coefficient d and the coefficient d are both four and the line AE and the line PQ are parallel, the vector data for one of the points on the line AE and one of the points on the line PQ may be simply represented by a distance from the other point on the line. In this case, the vector data is represented by scaler and the memory space for storing the vector data is saved.
It would be obvious that the present invention provides a facsimile transmission system wherein the compression of image data is achieved by using the rastervector conversion system shown in FIG. 5 in the transmission side and by using the vectorraster conversion system shown in FIG. 6 in the reception side.
FIG. 7 shows a printer controller for controlling an image printer in which the image data compression method of the present invention is applied. Referring to FIG. 7, the printer controller comprises a central processing unit (CPU) 11 connected to an input interface 13, a read only memory (ROM) 14, another ROM 15, a bit map memory 16 and an output interface 17 via a bus 12. The output interface 17 is connected to the printer (not shown). In operation, a print data specifying the letter to be printed as well as associated informations is supplied to the input interface 13. The ROM 14 stores a program for executing operation of Eq.(2) and the ROM 15 stores a letter data such as the coordinate of the initial and terminal points of curve portions forming the letter image, the initial and terminal points of the lines making the initial and terminal points of the line portions, and the like.
When a print data specifying a letter code and letter size is supplied to the input interface 13 from a processor and the like, the CPU 11 reads out the letter data from the ROM 15 on the bus 12 and calculates the coordinates which specify the curves and lines on the basis of the specified magnification factor. The coordinates thus obtained are transferred to the bit map memory 16. The CPU 11 then produces curves and lines according to the program stored in the ROM 14 using these coordinates, and writes the coordinate of the contour of the letter thus calculated into the bit map memory 16. Further, the CPU 11 performs area filling of the region thus surrounded by the contours according to the needs. Thus, there is formed the bit map of the letter in the memory 16. The bit map thus formed in the memory 16 is then sent to the printer or a plotter through the output interface 17 and the letter is printed on a sheet of paper.
The description for positional setting of the letter at the time of print out will be omitted as such a procedure is not pertinent to the subject matter of the present invention. Such a procedure is well known to those skilled in the art.
Further, the present invention is not limited to these embodiments described heretofore but various variations and modifications may be made without departing from the scope of the invention.
Claims (10)
A(1t).sup.3 +(cP(c3)A)(1t).sup.2 t+(dQ(d3 )E)(1t).sup.2 +Et.sup.3
A(1t).sup.3 +(cP(c3)A)(1t).sup.2 t+(dQ(d3)E)(1t).sup.2 +Et.sup.3
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US5223777A (en) *  19920406  19930629  AllenBradley Company, Inc.  Numerical control system for irregular pocket milling 
US5257016A (en) *  19900725  19931026  Brother Kogyo Kabushiki Kaisha  Apparatus for converting original character outline data including abridged special segment data, into normal character outline data 
US5280576A (en) *  19911224  19940118  Xerox Corporation  Method of adjusting the weight of a character of an outline font 
US5295203A (en) *  19920326  19940315  General Instrument Corporation  Method and apparatus for vector coding of video transform coefficients 
US5317681A (en) *  19911230  19940531  Xerox Corporation  Sequencing and scheduling moves for converting concave polyhedra to their convex hulls 
US5361333A (en) *  19920604  19941101  Altsys Corporation  System and method for generating selfoverlapping calligraphic images 
US5428717A (en) *  19911230  19950627  Xerox Corporation  Methods for converting concave polyhedra to their convex hulls 
US5438653A (en) *  19910820  19950801  Island Graphics Corporation  Method and system for color film separation preprocess using electronic objectbased choking and spreading procedures including object combining operations 
US5444825A (en) *  19910816  19950822  International Business Machines Corporation  Method and apparatus for scaling line patterns 
US5473742A (en) *  19940222  19951205  Paragraph International  Method and apparatus for representing image data using polynomial approximation method and iterative transformationreparametrization technique 
US5561534A (en) *  19910712  19961001  Canon Kabushiki Kaisha  Image processing method and apparatus 
US5610657A (en) *  19930914  19970311  Envistech Inc.  Video compression using an iterative error data coding method 
US5636337A (en) *  19910820  19970603  Island Graphics Corporation  Method and system for color film separation preprocess using electronic objectbased choking and spreading procedures including object combining operations 
US5640589A (en) *  19940408  19970617  Fujitsu Limited  Method and device for generating graphic data using a writing motion model 
US5754703A (en) *  19961216  19980519  Daewoo Electronics Co., Ltd.  Method for encoding a contour of an object in a video signal 
US5796924A (en) *  19960319  19980818  Motorola, Inc.  Method and system for selecting pattern recognition training vectors 
US5818963A (en) *  19940909  19981006  Murdock; Michael  Method and system for recognizing a boundary between characters in handwritten text 
US6057857A (en) *  19960612  20000502  Citrix Systems, Inc.  Method for the lossless compression of lines in a distributed computer system 
US6118899A (en) *  19951011  20000912  Citrix Systems, Inc.  Method for lossless bandwidth compression of a series of glyphs 
US6124863A (en) *  19920429  20000926  Canon Kabushiki Kaisha  Objectbased graphics system for displaying an image using explicit quadratic polynomial fragments 
US6141737A (en) *  19951011  20001031  Citrix Systems, Inc.  Method for dynamically and efficiently caching objects received from an application server by a client computer by subdividing cache memory blocks into equallysized subblocks 
US6226400B1 (en)  19980624  20010501  Colorcom, Ltd.  Defining color borders in a raster image by identifying and breaking contrast ties 
US6310970B1 (en)  19980624  20011030  Colorcom, Ltd.  Defining surfaces in border string sequences representing a raster image 
US6324300B1 (en)  19980624  20011127  Colorcom, Ltd.  Defining color borders in a raster image 
US20020029285A1 (en) *  20000526  20020307  Henry Collins  Adapting graphical data, processing activity to changing network conditions 
US6501855B1 (en)  19990720  20021231  Parascript, Llc  Manualsearch restriction on documents not having an ASCII index 
US6515763B1 (en)  19980731  20030204  Adobe Systems Incorporated  Vignette recognition and compression 
US6728399B1 (en)  19930809  20040427  Colorcom, Ltd.  Method and apparatus for defining color borders in a raster image by identifying and breaking contrast ties 
US20050198189A1 (en) *  20020314  20050908  Citrix Systems, Inc.  Methods and apparatus for generating graphical and media displays at a client 
US20060203007A1 (en) *  20050314  20060914  Citrix Systems, Inc.  A method and apparatus for updating a graphical display in a distributed processing environment using compression 
US20060206820A1 (en) *  20050314  20060914  Citrix Systems, Inc.  A method and apparatus for updating a graphical display in a distributed processing environment 
US20080033699A1 (en) *  20060804  20080207  Okuma Corporation  Program and method for generating approximate curve from approximate point group data 
US20090317011A1 (en) *  20060707  20091224  Telefonaktiebolaget Lm Ericsson (Publ)  Device and method for simplifying vector graphics 
US8671213B2 (en)  20020314  20140311  Citrix Systems, Inc.  Methods and apparatus for generating graphical and media displays at a client 
Citations (7)
Publication number  Priority date  Publication date  Assignee  Title 

US4254468A (en) *  19790503  19810303  Eltra Corporation  Typesetter character generating apparatus 
US4542412A (en) *  19820204  19850917  Shaken Co., Ltd.  Method for compressing character or pictorial image data 
US4566128A (en) *  19820913  19860121  Dainippon Screen Seizo Kabushiki Kaisha  Method for data compression for twovalue picture image 
US4620287A (en) *  19830120  19861028  Dicomed Corporation  Method and apparatus for representation of a curve of uniform width 
US4674058A (en) *  19811207  19870616  Dicomed Corporation  Method and apparatus for flexigon representation of a two dimensional figure 
US4907282A (en) *  19850913  19900306  Nhance Development Corporation  Method and apparatus for constructing, storing and displaying characters 
US4943935A (en) *  19870925  19900724  Kabushiki Kaisha Toshiba  Apparatus and method for plotting curved figures represented by high order functions in a bit map 
Patent Citations (7)
Publication number  Priority date  Publication date  Assignee  Title 

US4254468A (en) *  19790503  19810303  Eltra Corporation  Typesetter character generating apparatus 
US4674058A (en) *  19811207  19870616  Dicomed Corporation  Method and apparatus for flexigon representation of a two dimensional figure 
US4542412A (en) *  19820204  19850917  Shaken Co., Ltd.  Method for compressing character or pictorial image data 
US4566128A (en) *  19820913  19860121  Dainippon Screen Seizo Kabushiki Kaisha  Method for data compression for twovalue picture image 
US4620287A (en) *  19830120  19861028  Dicomed Corporation  Method and apparatus for representation of a curve of uniform width 
US4907282A (en) *  19850913  19900306  Nhance Development Corporation  Method and apparatus for constructing, storing and displaying characters 
US4943935A (en) *  19870925  19900724  Kabushiki Kaisha Toshiba  Apparatus and method for plotting curved figures represented by high order functions in a bit map 
Cited By (56)
Publication number  Priority date  Publication date  Assignee  Title 

US5257016A (en) *  19900725  19931026  Brother Kogyo Kabushiki Kaisha  Apparatus for converting original character outline data including abridged special segment data, into normal character outline data 
US5561534A (en) *  19910712  19961001  Canon Kabushiki Kaisha  Image processing method and apparatus 
US5444825A (en) *  19910816  19950822  International Business Machines Corporation  Method and apparatus for scaling line patterns 
US5636337A (en) *  19910820  19970603  Island Graphics Corporation  Method and system for color film separation preprocess using electronic objectbased choking and spreading procedures including object combining operations 
US5438653A (en) *  19910820  19950801  Island Graphics Corporation  Method and system for color film separation preprocess using electronic objectbased choking and spreading procedures including object combining operations 
US5280576A (en) *  19911224  19940118  Xerox Corporation  Method of adjusting the weight of a character of an outline font 
US5428717A (en) *  19911230  19950627  Xerox Corporation  Methods for converting concave polyhedra to their convex hulls 
US5317681A (en) *  19911230  19940531  Xerox Corporation  Sequencing and scheduling moves for converting concave polyhedra to their convex hulls 
US5295203A (en) *  19920326  19940315  General Instrument Corporation  Method and apparatus for vector coding of video transform coefficients 
US5223777A (en) *  19920406  19930629  AllenBradley Company, Inc.  Numerical control system for irregular pocket milling 
US6124863A (en) *  19920429  20000926  Canon Kabushiki Kaisha  Objectbased graphics system for displaying an image using explicit quadratic polynomial fragments 
US5361333A (en) *  19920604  19941101  Altsys Corporation  System and method for generating selfoverlapping calligraphic images 
US6728399B1 (en)  19930809  20040427  Colorcom, Ltd.  Method and apparatus for defining color borders in a raster image by identifying and breaking contrast ties 
US5610657A (en) *  19930914  19970311  Envistech Inc.  Video compression using an iterative error data coding method 
US5473742A (en) *  19940222  19951205  Paragraph International  Method and apparatus for representing image data using polynomial approximation method and iterative transformationreparametrization technique 
US5640589A (en) *  19940408  19970617  Fujitsu Limited  Method and device for generating graphic data using a writing motion model 
US5818963A (en) *  19940909  19981006  Murdock; Michael  Method and system for recognizing a boundary between characters in handwritten text 
US6118899A (en) *  19951011  20000912  Citrix Systems, Inc.  Method for lossless bandwidth compression of a series of glyphs 
US6141737A (en) *  19951011  20001031  Citrix Systems, Inc.  Method for dynamically and efficiently caching objects received from an application server by a client computer by subdividing cache memory blocks into equallysized subblocks 
US5796924A (en) *  19960319  19980818  Motorola, Inc.  Method and system for selecting pattern recognition training vectors 
US6057857A (en) *  19960612  20000502  Citrix Systems, Inc.  Method for the lossless compression of lines in a distributed computer system 
US6172683B1 (en)  19960612  20010109  Citrix Systems, Inc.  Method for the lossless compression of lines in a distributed computer system 
US5754703A (en) *  19961216  19980519  Daewoo Electronics Co., Ltd.  Method for encoding a contour of an object in a video signal 
US6226400B1 (en)  19980624  20010501  Colorcom, Ltd.  Defining color borders in a raster image by identifying and breaking contrast ties 
US6310970B1 (en)  19980624  20011030  Colorcom, Ltd.  Defining surfaces in border string sequences representing a raster image 
US6324300B1 (en)  19980624  20011127  Colorcom, Ltd.  Defining color borders in a raster image 
US6515763B1 (en)  19980731  20030204  Adobe Systems Incorporated  Vignette recognition and compression 
US6501855B1 (en)  19990720  20021231  Parascript, Llc  Manualsearch restriction on documents not having an ASCII index 
US6917709B2 (en)  19990720  20050712  Parascript Llc  Automated search on cursive records not having an ASCII index 
US7490166B2 (en)  20000526  20090210  Citrix Systems, Inc.  Remote control of a client's offscreen surface 
US20030046432A1 (en) *  20000526  20030306  Paul Coleman  Reducing the amount of graphical line data transmitted via a low bandwidth transport protocol mechanism 
US20020029285A1 (en) *  20000526  20020307  Henry Collins  Adapting graphical data, processing activity to changing network conditions 
US20090144292A1 (en) *  20000526  20090604  Henry Collins  Method and system for efficiently reducing graphical display data for transmission over a low bandwidth transport protocol mechanism 
US7028025B2 (en)  20000526  20060411  Citrix Sytems, Inc.  Method and system for efficiently reducing graphical display data for transmission over a low bandwidth transport protocol mechanism 
US20020035596A1 (en) *  20000526  20020321  Ruiguo Yang  Remote control of a client's offscreen surface 
US8290907B2 (en)  20000526  20121016  Citrix Systems, Inc.  Method and system for efficiently reducing graphical display data for transmission over a low bandwidth transport protocol mechanism 
US7127525B2 (en)  20000526  20061024  Citrix Systems, Inc.  Reducing the amount of graphical line data transmitted via a low bandwidth transport protocol mechanism 
US7502784B2 (en)  20000526  20090310  Citrix Systems, Inc.  Method and system for efficiently reducing graphical display data for transmission over a low bandwidth transport protocol mechanism 
US8099389B2 (en)  20000526  20120117  Citrix Systems, Inc.  Method and system for efficiently reducing graphical display data for transmission over a low bandwidth transport protocol mechanism 
US20100205246A1 (en) *  20000526  20100812  Henry Collins  Method and system for efficiently reducing graphical display data for transmission over a low bandwidth transport protocol mechanism 
US20080201405A1 (en) *  20020314  20080821  Citrix Systems, Inc.  Method and System for Generating a Graphical Display for a Remote Terminal Session 
US7376695B2 (en)  20020314  20080520  Citrix Systems, Inc.  Method and system for generating a graphical display for a remote terminal session 
US8671213B2 (en)  20020314  20140311  Citrix Systems, Inc.  Methods and apparatus for generating graphical and media displays at a client 
US20050198189A1 (en) *  20020314  20050908  Citrix Systems, Inc.  Methods and apparatus for generating graphical and media displays at a client 
US8131817B2 (en)  20020314  20120306  Citrix Systems, Inc.  Method and system for generating a graphical display for a remote terminal session 
US9325759B2 (en)  20020314  20160426  Citrix Systems, Inc.  Methods and apparatus for generating graphical and media displays at a client 
US8131816B2 (en)  20020314  20120306  Citrix Systems, Inc.  Methods and apparatus for generating graphical and media displays at a client 
US8423673B2 (en)  20050314  20130416  Citrix Systems, Inc.  Method and apparatus for updating a graphical display in a distributed processing environment using compression 
US20060203007A1 (en) *  20050314  20060914  Citrix Systems, Inc.  A method and apparatus for updating a graphical display in a distributed processing environment using compression 
US8677022B2 (en)  20050314  20140318  Citrix Systems, Inc.  Method and apparatus for updating a graphical display in a distributed processing environment using compression 
US20060206820A1 (en) *  20050314  20060914  Citrix Systems, Inc.  A method and apparatus for updating a graphical display in a distributed processing environment 
US8171169B2 (en)  20050314  20120501  Citrix Systems, Inc.  Method and apparatus for updating a graphical display in a distributed processing environment 
US8213732B2 (en) *  20060707  20120703  Telefonaktiebolaget Lm Ericsson (Publ)  Device and method for simplifying vector graphics 
US20090317011A1 (en) *  20060707  20091224  Telefonaktiebolaget Lm Ericsson (Publ)  Device and method for simplifying vector graphics 
US7792603B2 (en) *  20060804  20100907  Okuma Corporation  Program and method for generating approximate curve from approximate point group data 
US20080033699A1 (en) *  20060804  20080207  Okuma Corporation  Program and method for generating approximate curve from approximate point group data 
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